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Figure 4 is illustrating a simplified co-current rotary dryer – representative of RD101. The

reasons for choosing a co-current (and not counter-current) dryer are listed below:

1. Co-current is suitable for drying of particles with high surface moisture; note, TiO2 slag

particles are non-porous with most of the moisture on its surface (Rowson, 2017).

2. Counter-current significantly affects discharge velocity for particles with

d50<0.5mm.
3. Co-current air flow results in a cooler surface temperature of the dryer shell, leading to
lesser loss due to radiation and safer working environment.
4. With co-current it is easier to control the temperature of the solid content.
Rotary dryers act as heat exchanger simultaneously conveying solid particulates, and their
loading has critical effect on particle transport. Table 9 summarizes the three loading types
and their effect on particle transport.
As can be seen from figure 6, design-loading provides solid cascade across maximum possible
chamber cross-section, hence the best gas-solid contacting area. Therefore, RD101 will be
designed to achieve design-loading.
3.2 energy balance:
Sometimes for the calculation of heat for moisture (Q1), and heat for vapour (Q3) instead of
boiling point of water ( ), the wet bulb temperature of inlet air ( ) is used (see equations 1 and
3) (Mujumdar, 2007). Although, it does not significantly affect the energy values, to minimise
the errors in design of RD101 average values obtained from the two approaches will be used.
The new values for Q, G and Q are presented in table10. Appendix B tabulates the difference in
the values obtained via the two methods. For direct-heat rotary dryers thermal efficiency ranges
from 50% to 75% (Mujumdar, 2007). Thermal efficiency under our energy values is 0.54 ∙ 100%
≈ 54%, hence acceptable.
3.3. Drying time
Particle that is being dried is composed mainly of TiO2 which is a non-porous material with 80%
– 90% of the moisture on its surface (Rowson, 2017). Thus, drying rate is assumed to be affected
85% by constant and 15% by falling rate; and using equation 10 (Spyropoulos, 2017) the drying
time (td) is evaluated to be 144 seconds.
3.4. Internal and effective dryer diameter
Cylindrical dryer shell internal diameter (Di) is calculated by equation 11.1. (Mujumdar, 2007),
which accounts for the following:
1. It must be sufficiently large to avoid product entrainment (i.e. air mass velocity does not
2.
exceed the maximum allowable air flux ̇ (kg/m2s)).
Only a fraction of dryer cross section is used by the air to flow and is about 0.85.
The maximum allowable air mass flux, depends on particle settling velocity (up), where to avoid
significant particle shifts (and entrainment), (air velocity) must be less than the up (Matchett &
Baker, 1987). To allow for safe fluctuations in air flow control will be taken as half of u p value.
The particle settling velocity, thus air mass flux are found through series of calculations
using equations 11.2 – 11.5 (Barigou, 2018):
Finally, using the value of ̇ with equation 11.1., the required internal diameter, Di, is calculated
as 2.1 m, of which 1.8 m is the effective diameter, De. In general, dryer diameters commonly
range from 1 to 3 metre (Peter, Julian, & Mccabe, 1993), thus the result is acceptable.
3.5.1. Number of flights and residence time
Purpose of flights in a rotary dryer is to provide intimate contact between moist solid particles
and hot gas stream by lifting and showering the particles. For efficient use of dryer volume, the
required number of flights, nf, must be three times the diameter of the dryer (in feet) (S.J.
Friedman & W.R. Marshall, 1949) and is calculated as follows:
The particles retained in the dryer drum will be distributed to 21 flights, hence in each flight
fraction of material, fm, will be 0.0476 (calculated by dividing 1 by 27).
Considering constant (dynamic) rotation of the dryer, f m in each flight can be assumed same as
fraction of material in drying zone. Hence, the residence time required is calculated as below
(Ingram A. , 2018):
Typical residence time ranges at 5 –90 minutes (Couper, Penny, Fair, & Waals, 2005). Hence,
the value may be accepted.
3.5.2. Volume of material and the dryer
The volume of material in the dryer, as given in equation 13, is the volumetric flow rate of
material (per minute) times the required residence time for drying.
Based on industrial experience, most efficient drying performance (i.e. design loading) is
achieved when the total amount of solid in the rotary drum is 8% – 12% of its volume (Weiss,
1985). Taking it to be 8%, the dryer volume needs to be 31.71m3.
3.5.3. Dryer length
Calculation of the length from dryer volume and cross sectional area:
Acceptableindustrialrotarydryerlengthtodiameterratioliesbetween4and10 (Weiss,1985).The
obtained ratio is 4.36, hence suitable.
3.5.4. Dryer rotational speed and inclination
Peripheral speed values for rotary dryers ranges from 0.1 to 0.5 m/s (van'tLand, 2012) and the
common speed of rotation for given size is usually between 2 and 5 rpm (Lisboa, Vitorino,
Delaiba, Finzer, & Barrozo, 2007). To get speed of rotation 5rpm, peripheral speed is taken as
0.175 m/s.
A correlation for residence time as a function of other parameters in a co-current rotary dryer is
given in equation 16 (S.J. Friedman & W.R. Marshall, 1949). Although the air velocity is chosen
to avoid particle entrainment, it has some drag effect on the falling particles and the second term
in the correlation accounts for this, hence minimising design error.
Rearranging the correlation, required inclination of the dryer is found to be 0.4o.
3.6.1. Desirable dryer length
For efficient use of energy in the air stream, length of a dryer may be found via correlation given
in equation 17. (Where the energy unit is in Btu, length in ft, mass in lb and the log mean
temperature difference, ∆ , is between the wet-bulb depressions of the drying air at the inlet and
outlet of the dryer in unit of Kelvin (Mujumdar, 2007). Rearranging the equation for L and
following unit conversions, the length equals to 15.1m. The obtained length to diameter ratio is
now 7.2, hence suitable.
3.6.2. Residence time
Time required for particle to be retained in the dryer to meet desired reduction in its moisture
content depends on particle drying time and the time it contacts the air per fall from flight per
rotation of the cylindrical drum (per minute). To calculate time particle contacts the air stream
per fall, tf[s],the following equation is used:
Assuming every particle falls once per rotation of the dryer and taking the rotational speed,
N=5rpm, then:
➢ Per 1 minute particle contacts hot air for 2.05 seconds (i.e. tc= × ).
➢ To contact air for 144 seconds, about 70.5 minutes of residence is required (i.e. 351
rotations). This residence time is within acceptable range of 5 – 90 minutes.
3.6.3. Dryer inclination
Using the previous correlation 16, required inclination of the dryer with given length and
residence time is slightly higher than in method 1, and is 0.45o. As both, the residence time and
the length in design method 2 have increased, and as it is their ratio what affects the inclination,
there is only fractional increase in the dryer inclination. (Note, the assumed speed of rotation is
same in both methods).
3.6.4. Dryer and material volume
Rearranging equation 15, this method gives dryer volume of 52.3 m3. And using equation 14,
the volume of the material held-up in the dryer becomes 3.55 m3. Thus, now the loading is 6.8%
of the dryer volume. Hence, as table 9 states, bouncing of particles may occur, what may bring
particles of higher moisture content to the product stream.
To reach a better design with method 2, set of graphs are plotted and computation s made as
presented in table 11. Final design values from method 2 (and method 1) is presented in table 12.
i. The length range between 8– 13 metre provides design loading.
ii. Reduction in N increases the .
iii.
Increase in increases the volume hold up (figure 10).
iv.
To reduce the length, either of inclination or rotation speed must be reduced to maintain
the residence time (see equation 16).
v. Hence, keep the length unchanged.
vi.
Take minimum allowable rpm for the given design (i.e. N=4rpm, see figure 9).
Recalculating: loading becomes 8.5%, while having other parameters within acceptable range.
3.7. Comparing the two design methods and final decision
Design achieved by both of the methods discussed above give values applicable within industry.
However, dryer designed through method 1 is chosen more efficient due to reasons stated below.
Looking at the dryer volumes obtained via two approaches, method 1 is more preferable as it is
smaller. Smaller volume does not only bare lower capital cost, but also consumes less power
(due to its lighter weight), thus giving lower operating cost.
Dryer from method 1 has a lower residence time, hence making the control more re liable by
having smaller dead time (see control section).
Closely examining the two design methods, it is found that the second method lacks efficient use
of its volume. In dryer designed with method 2 material spends more time in the bulk (of
particles) than at falling (contacting the hot air). This is due to the assumption that every particle
falls just once per rotation, which in reality is not acceptable assumption as it does not cover
number of flights in the dryer. Consequently, this two methods also emphasize the significance
of flight implementation and particle showering in a direct contact rotary dryer.
The figure 11 is a characteristic sketch of raw and actual drying curves, where for the preferred
method 1 total time spent by particle in the bulk and falling from the flights equal to 48.4 minute
and 2 minutes respectively.
3.8.1. Pressure drop
It is expected to have main pressure drop through the dryer due to the air acceleration and wall
friction, which are first and second terms of the equation 19 respectively.
The given pressure drop is negligible and indicates that the operation of the rotary dryer is safe .
However, mechanical seals will be employed at both ends of the dryer to avoid air
leakage. Note: in fact the voidage is less than 1 due to constant particle showering, hence in
reality ∆P is also less than above.
3.8.2. Flight design
Considering low moisture content of the material (i.e. it is non-sticky) and the design loading of
the dryer, flights with right angles are chosen due to their suitability.
From section 3.5.1 it is known that each flight must accommodate 0.0476 fraction of the material
held in the dryer. Having the length of the dryer 9.16 m, the fraction of material per length of a
flight needstobe0.0052. Thus,thevolumetricholdup(permetre),h*=Vp×0.0052=0.0132.
Flight radial depth must be 8 times smaller than the Di (DCP Manufacturing Co., Inc.), hence is
0.262m. Its lip height may be taken as half of the depth.
Using equation 20, with α=0o (i.e. at maximum loading), required angle between horizontal and
free surface of solids is calculated. Figure 12 illustrates the symbols in equation 20 and table 13
provides their values.
Note: in a very small section of the dryer length from the particle inlet side, flights are made
spiral to distribute the particles entering the dryer to the flights.
3.8.3. Dryer shell thickness
Recalling the shell material was chosen to be carbon steel (grade c), the shell thickness is
calculated using equation 21 (DCP Manufacturing Co., Inc.), considering the following:
The operation of the dryer is assumed isobaric, therefore design pressure must be taken as
170,254 Pa(Rushton&Hesse,1962).
Double welded butt joints are suitable, but need polishing from the inner side to avoid
entrapment of solid particulates (Smith, 1984). This will have joint efficiency, je, 0.7.
Corrosion is a major problem in carbon steels. Its average corrosion rate is 0.3 mm/yr
(Theodore, 2008). Therefore, corrosion allowance of 6.35 mm may be taken (Rushton & Hesse,
1962).
Minimum shell thickness (including its corrosion allowance) for vessels of diameter range s from
2 to 2.5metreis9mm(Sinnot,2004). Hence, the calculated thickness is acceptable.
The carbon steel thermal conductivity is comparatively high, kA=51.9 W/mK, and needs an
insulation. Considering resistance to thermal shock, low density and thermal conductivity,
(kB=0.17W/mK), of ceramic fibres, they will be used as insulating material (Nicolau & Dadam,
2009).
To calculate the required thickness of insulating layer, equation 22 is used. Figure 12 is
illustrating the symbols used.
3.8.7. Dryer support and drive
As shown in the mechanical drawing figure 16, the dryer is to be supported on three concrete
base seats. The middle seat accommodates mechanism rotating the dryer shell as given in figure
14, including the following:
1. Girth gear directly mounted on the dryer shell;
2. Pinion gear to drive the girth gear;
3. Speed reducer to adjust the usable work;
4. Drive motor to provide the power.
The two side seats hold carrying rollers, which are supporting the dryer shell assembly (i.e.
holding the load) while maintaining its rotation via tires, made of cast steel, mounted onto the
dryer shell (Weiss, 1985). To avoid tires running off the supporting rollers, thrust rollers are used
as shown in figures 15 and 16.
Having supports at two ends allow for certainty in prediction of loading distribution. Assuming
the dryer loading is evenly distributed, as its inclination is not large. Loading on each side seat
must hold: 7534 ∙ = . . The loading of the dryer will have longitudinal bending stress
at its mid-span (at about L=4.58 metre). To equalize the bending moment magnitude at the midspan with moment from the supports, their position along the dryer must be at 21% of the span
(Sinnot, 2004). Thus, the side supports will be positioned at 1.9 metre from the end. It must be
noted that the stiffening effect close to the ends of the cylindrical geometry of the dryer
overcomes bending effects (Ross, 1999).
To calculate power required to drive the dryer with flights equation 24, proposed by CE
Raymond Division, Combustion Engineering Inc., can be used (Mujumdar, 2007).
For dryers rotating at peripheral speed range of 0.1 to 0.5 m/s, motive powe r can be found using
equation 25 (van't Land, 2012). RD101 peripheral speed is 0.175 m/s hence, equation may be
used.
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